arXiv 0911.06952009-11-03quant-ph

量子理论及以后：纠缠是特殊的吗？

Quantum Theory and Beyond: Is Entanglement Special?

Borivoje Dakic, Caslav Brukner

备注：: 14 pages, 4 figures
发表信息：: Deep Beauty: Understanding the Quantum World through Mathematical Innovation, Ed. H. Halvorson (Cambridge University Press, 2011) 365-392

摘要：

量子理论做出了最准确的经验预测，但它缺乏简单、可理解的物理原理，而这些物理原理可以唯一地导出量子理论。存在着一个广泛的概率理论，它们都与量子理论有一些共同的特征，例如对个体结果的概率预测（不确定性），信息传输不可能超过光速（无信号）或不可能复制未知状态（无克隆）。绝大多数试图寻找量子理论背后的物理原理的尝试，要么不能从原理中唯一地推导出理论，要么是基于抽象的数学假设，这些假设需要更确凿的物理动机。在这里，我们证明了经典概率论和量子理论可以从三个合理的公理中重建：（1）（信息容量）所有信息承载能力为一位的系统都是等效的。(2)（局部性）复合系统的状态完全由子系统的测量决定。(3)（可逆性）在任何两个纯态之间存在可逆变换。如果要求从最后一个公理的变换是连续的，那么就把量子理论从经典概率论中分离出来。从我们的重建中得出的一个显著结果是，除了量子理论之外，没有任何概率理论可以在不违背一个或多个公理的情况下展示纠缠。

英文摘要：

Quantum theory makes the most accurate empirical predictions and yet it lacks simple, comprehensible physical principles from which the theory can be uniquely derived. A broad class of probabilistic theories exist which all share some features with quantum theory, such as probabilistic predictions for individual outcomes (indeterminism), the impossibility of information transfer faster than speed of light (no-signaling) or the impossibility of copying of unknown states (no-cloning). A vast majority of attempts to find physical principles behind quantum theory either fall short of deriving the theory uniquely from the principles or are based on abstract mathematical assumptions that require themselves a more conclusive physical motivation. Here, we show that classical probability theory and quantum theory can be reconstructed from three reasonable axioms: (1) (Information capacity) All systems with information carrying capacity of one bit are equivalent. (2) (Locality) The state of a composite system is completely determined by measurements on its subsystems. (3) (Reversibility) Between any two pure states there exists a reversible transformation. If one requires the transformation from the last axiom to be continuous, one separates quantum theory from the classical probabilistic one. A remarkable result following from our reconstruction is that no probability theory other than quantum theory can exhibit entanglement without contradicting one or more axioms.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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